Question

The current of a stream runs at the rate of 4 km an hour. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in

still water is:

• A. $6km/hr$
• B. $7.5km/hr$
• C. $8km/hr$
• D. $6.8km/hr$

Answer 1

Answer: (C)

$8km/hr$

Let the speed of a boat in still water$=\alpha$ km/hr

Given speed of water(stream)$=4$ km/hr

Speed of boat during downstream$=(\alpha +4)$km/hr

Speed of boat during upstream$=(\alpha -4)$km/hr

Time to travel $6$km during downstream$=\frac{6}{\alpha +4}$hr

Time to travel $6$km during upstream$=\frac{6}{\alpha -4}$hr

Given $\frac{6}{\alpha +4}+\frac{6}{\alpha -4}=2$

$3\left[\frac{\alpha +4+\alpha -4}{(\alpha +4)(\alpha -4)}\right]=1$

$\Rightarrow 6\alpha ={\alpha }^2-16$

$\Rightarrow {\alpha }^2-8\alpha +2\alpha -16=0$

$\Rightarrow (\alpha -8)(\alpha +2)=0$

$\alpha =8\ne -2$

Speed of a boat in still water$=8$km/hr

Speed $>0$.